{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "# 伽辽金法重解例题3\n",
    "\n",
    "\n",
    "姚端正、周国全、贾俊基《数学物理方法》第四版P.275\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b0f74b2-86df-4e0d-b78c-0f7aa49ac37d",
   "metadata": {},
   "source": [
    "## 1、导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy 包中所有的函数\n",
    "from sympy.abc import x,y # 引入默认的符号变量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e607055d-a10b-44ca-9c6b-af96bd308e26",
   "metadata": {},
   "source": [
    "## 2、定义参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3ee6933f-d63d-45d9-bf17-0930ab30bf09",
   "metadata": {},
   "outputs": [],
   "source": [
    "c0,c1,lamd = symbols('c0 c1 lambda') # 自定义符号变量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e564343b-e7cd-472b-a531-776d5610b3b9",
   "metadata": {},
   "source": [
    "## 3、泛函"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a4538ea-5c61-4400-ba37-6bd8ca4d0d75",
   "metadata": {},
   "source": [
    "基函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b1db7b4c-a630-474c-8c8a-0e2f2e33cc43",
   "metadata": {},
   "outputs": [],
   "source": [
    "v1 = x*(x-1)\n",
    "v2 = x**2 *(x-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3afd194f-2442-430f-8493-6861952a8c01",
   "metadata": {},
   "source": [
    "试探解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9cea2f4e-9546-4a20-96e6-469cc7a6b2df",
   "metadata": {},
   "outputs": [],
   "source": [
    "ux = c0*v1+c1*v2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10d6f9b6-f93c-4ac5-a95e-49b2ae736b1e",
   "metadata": {},
   "source": [
    "计算泛函"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "81a5c4fa-ff42-41c2-ba96-ca44ec677482",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{3} + \\frac{c_{1}}{6} - \\lambda \\left(\\frac{c_{0}}{30} + \\frac{c_{1}}{60}\\right)$"
      ],
      "text/plain": [
       "c0/3 + c1/6 - lambda*(c0/30 + c1/60)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J_1  = integrate(diff(ux,x)*diff(v1,x),(x, 0, 1)) - lamd* integrate(ux*v1,(x, 0, 1))\n",
    "J_1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "edc2a25b-7805-4bd7-9f56-3c99c6fa5bdf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{6} + \\frac{2 c_{1}}{15} - \\lambda \\left(\\frac{c_{0}}{60} + \\frac{c_{1}}{105}\\right)$"
      ],
      "text/plain": [
       "c0/6 + 2*c1/15 - lambda*(c0/60 + c1/105)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J_2  =  integrate(diff(ux,x)*diff(v2,x),(x, 0, 1)) - lamd* integrate(ux*v2,(x, 0, 1))\n",
    "J_2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "266e5c6b-0459-4376-bdfe-56bc53c3ca62",
   "metadata": {},
   "source": [
    "计算系数矩阵，先定义2*2零矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "19071805-db55-4ac0-b6d1-99449c30a5e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0],\n",
       "[0, 0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c=zeros(2)\n",
    "matrix_c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebde8522-9623-45a4-aab5-d8b40ed817ca",
   "metadata": {},
   "source": [
    "计算参数前面的系数，填入上面的零矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "de5a1f7c-c568-49d8-9a61-42411ed5c9dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [c0,c1] # 参数列表\n",
    "J = [J_1,J_2] # 泛函列表\n",
    "for i in [0,1]:\n",
    "    for j in [0,1]:\n",
    "        matrix_c[i,j]= expand(J[i]).coeff(c[j])\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "26353137-749f-4f00-8fbc-7df8633c1c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{3} - \\frac{\\lambda}{30} & \\frac{1}{6} - \\frac{\\lambda}{60}\\\\\\frac{1}{6} - \\frac{\\lambda}{60} & \\frac{2}{15} - \\frac{\\lambda}{105}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1/3 - lambda/30,   1/6 - lambda/60],\n",
       "[1/6 - lambda/60, 2/15 - lambda/105]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c6e2920-a730-4782-b3cd-b3326b7ef8ef",
   "metadata": {},
   "source": [
    "查看待求矩阵的行列式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "41ea76a9-df1f-4662-b538-903745ae24d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\lambda^{2}}{25200} - \\frac{13 \\lambda}{6300} + \\frac{1}{60}$"
      ],
      "text/plain": [
       "lambda**2/25200 - 13*lambda/6300 + 1/60"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c.det()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9480a1a-4b50-4fe9-8fe1-d0d07d5e477e",
   "metadata": {},
   "source": [
    "求解本征值$\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4b7aea0c-06b2-4aec-a70b-83b5fa415006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 42]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd = solve(matrix_c.det(),lamd)\n",
    "sol_lamd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb8309c2-0d56-447e-99d3-fb8470c30e69",
   "metadata": {},
   "source": [
    "计算归一化条件方程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2805e586-4b89-4da4-8641-9284c575db05",
   "metadata": {},
   "outputs": [],
   "source": [
    "condition = integrate(ux*ux,(x, 0, 1)) -1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06c3c30f-ffd4-4a93-ad34-f4e3e517d406",
   "metadata": {},
   "source": [
    "把第一个本征值带入方程组求解参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f5f452d0-820a-46ce-927b-22cb3c1e44eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(30), 0), (sqrt(30), 0)]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_1=[J_1.subs(lamd,sol_lamd[0]), J_2.subs(lamd,sol_lamd[0]),condition]\n",
    "c_sols_1 = solve(eqs_1, c0,c1)\n",
    "c_sols_1 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd972c25-fcb3-464e-9275-55dd9ebec20b",
   "metadata": {},
   "source": [
    "把第二个本征值带入方程组求解参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "217615b0-b8c5-4d71-8649-cf10c54fa08a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(210), 2*sqrt(210)), (sqrt(210), -2*sqrt(210))]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_1=[J_1.subs(lamd,sol_lamd[1]), J_2.subs(lamd,sol_lamd[1]),condition]\n",
    "c_sols_2 = solve(eqs_1, c0,c1)\n",
    "c_sols_2 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c55b596-56ca-45fa-982b-d64c2f3faf9a",
   "metadata": {},
   "source": [
    "## 4、作图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6ef2fbce-3548-4085-897c-716e5217dd7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x239fb5391d0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ux_1=ux.subs([(c0,c_sols_1 [0][0]), (c1,c_sols_1 [0][1])])# 基态试探解\n",
    "ux_ex_1=sqrt(2) *sin(pi* x) # 基态精确解\n",
    "plot(ux_1,ux_ex_1,(x,0,1),legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ec0b3a52-3e75-4621-86fa-7d3d3b511088",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x2398a609210>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ux_2=ux.subs([(c0,c_sols_2 [0][0]),(c1,c_sols_2 [0][1])])# 第一激发态试探解\n",
    "ux_ex_2=sqrt(2) *sin(2*pi* x) # 第一激发态精确解\n",
    "plot(ux_2,ux_ex_2,(x,0,1),legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "46de5305-46ca-4da4-813b-85cd4bdf9af9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "681fdbdf-7841-4ed1-b534-7a19de29abb2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
